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MathCalculus

Antiderivative of 1/x: Evaluate ∫2/x dx

Evaluate OpenStax Calculus Volume 1 exercise 325 using the antiderivative of 1/x and explain why absolute value and x ≠ 0 matter.

Question

OpenStax Calculus Volume 1, §5.6, exercise 325: Compute the indefinite integral

∫2x dx.\int\frac{2}{x}\,dx.

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Evidence boundary

The source supplies no initial condition and excludes x=0x=0 through the integrand. A general antiderivative on the disconnected domain can have a different constant on each side of zero.